Published Wednesday, 18 January 2012
Mr Elliott commented in response to comments made by the DUP leader Peter Robinson's comments in an interview earlier this week.
Mr Robinson told UTV's Political Editor Ken Reid that he would welcome a single unionist party.
On Wednesday, Mr Elliott said his party had "always sought to act in the best interest of Northern Ireland and its people".
"The Ulster Unionist Party believes that Northern Ireland's interests are best served by the maintenance of the Union with Great Britain. I assume all parties trading under the Unionist name believe the same," he said.
Mr Elliott added that he agreed with Mr Robinson "on that fundamental point" but there are other issues on which the parties disagree, including the reform of local government from 26 to 11 councils.
He said he has reservations about the merit of having one unionist party for Northern Ireland.
"I have always questioned whether or not a single party would deliver the required electoral success for Unionism.
"For example, the choice provided by the existence of the UUP, DUP and TUV may actually encourage more Unionist voters to go to the polls.
"Certainly an agreed pro-Union Westminster candidate in Fermanagh and South Tyrone in 2010 did not maximise Unionist voter turnout and actually polled fewer votes than the Ulster Unionist and the DUP got between them at both the 2011 local government and Assembly elections," said Mr Elliott.
The UUP leader that he has met with the leaders of the DUP, TUV, Alliance party and SDLP, but he said the issue between parties is based on more than a good relationship involving the leaders.
"I have in the past requested meetings with Mr Robinson to discuss issues such as the Justice Review and proposed changes to Parliamentary boundaries.
"This is of course about more than whether or not Peter Robinson has a good relationship with me, or whether or not the DUP work well with Danny Kennedy in the Executive.
"It is about how the DUP work with Ulster Unionists on Stormont Committees and in Council Chambers across Northern Ireland. It is about respect and trust and actions speak louder than words.
"If any proposals come forward the Ulster Unionist Party will obviously assess them.
"We will continue to act in the best interest of both Northern Ireland and Unionism," he added.